Estimating low sampling frequency risk measure by high-frequency data - Niels Wesselhöfft; Wolfgang Karl Härdle (Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series", 2019)
Weekly, quarterly and yearly risk measures are crucial for risk reporting according to Basel III and Solvency II. For the respective data frequencies, the authors show in a simulation and backtest study that available data series are not sufficient in order to estimate Value at Risk and Expected Shortfall sufficiently, given confidence levels of 99.9% and 99.99%. Accordingly, this paper presents a semi-parametric estimation method, rescaling data from high- to low-frequency which allows to obtain significantly more data points for the estimation of the respective risk measures. The presented methodology in the α-stable framework, which is able to mimic multifractal behavior in asset returns, provides tail events which never occurred in the original low-frequency dataset.
Keywords: C14; C22; C46; C53; G32; 330; high-frequency; multifractal; stable distribution; rescaling; risk management; Value at Risk; quantile distribution